On the category of L-fuzzy automata, coalgebras and dialgebras

摘要

This paper is towards the study of L-fuzzy automata from the categorical point of view, where Lis a complete residuated lattice. We introduce a functor having both the left/right adjoint from the category of L-fuzzy Sigma-semiautomata LFSA(Sigma) to the category-LFTCRL(Sigma), a category of complete residuated lattices corresponding to L-fuzzy Sigma-semiautomata. The L-fuzzy response map of an L-fuzzy automaton leads us to provide a characterization of an L-fuzzy regular language. Interestingly, we show that the category LFSA(Sigma) is a category of T-1-coalgebras/(T-2, T-3)-dialgebras. Moreover, we establish a relationship between the category of T-1-coalgebras and the category of (T-2, T-3)-dialgebras. (C) 2020 Elsevier B.V. All rights reserved.